Vascular catheterizations, such as coronary catheterizations, are frequently-performed medical interventions. Such interventions are typically performed in order to diagnose the blood vessels for potential disease, and/or to treat diseased blood vessels. Typically, in order to facilitate visualization of blood vessels, the catheterization is performed under extraluminal imaging. Typically, and in order to highlight the vasculature during such imaging, a contrast agent is periodically injected into the applicable vasculature. The contrast agent typically remains in the vasculature only momentarily. During the time that the contrast agent is present in the applicable vasculature, the contrast agent typically hides, in full or in part, or obscures, devices positioned or deployed within that vasculature.
The following articles do not necessarily pertain to medical procedures or body organs, but yet serve as a useful technical background.
An article entitled “Nonlocal linear image regularization and supervised segmentation,” by Gilboa and Osher (SIAM Multiscale Modeling & Simulation, volume 6, issue 2, pp. 595-630, 2007), which is incorporated herein by reference, describes how a nonlocal quadratic functional of weighted differences is examined. The weights are based on image features and represent the affinity between different pixels in the image. By prescribing different formulas for the weights, one can generalize many local and nonlocal linear de-noising algorithms, including the nonlocal means filter and the bilateral filter. In this framework one can show that continuous iterations of the generalized filter obey certain global characteristics and converge to a constant solution. The linear operator associated with the Euler-Lagrange equation of the functional is closely related to the graph Laplacian. Thus, the steepest descent for minimizing the functional as a nonlocal diffusion process may be determined. This formulation allows a convenient framework for nonlocal variational minimizations, including variational denoising, Bregman iterations and the recently-proposed inverse-scale-space. The authors demonstrate how the steepest descent flow can be used for segmentation. Following kernel based methods in machine learning, the generalized diffusion process is used to propagate sporadic initial user's information to the entire image. The process is not explicitly based on a curve length energy and thus can cope well with highly non-convex shapes and corners. Reasonable robustness to noise is achieved.
An article entitled “Nonlocal Operators with Applications to Image Processing,” by Gilboa and Osher (SIAM Multiscale Modeling & Simulation, volume 7, issue 3, pp. 1005-1028, 2008), which is incorporated herein by reference, describes the use of nonlocal operators to define types of flows and functionals for image processing and other applications. The authors describe a main advantage of the technique over classical Partial-Differential-Equation-based (PDE-based) algorithms as being the ability to handle better textures and repetitive structures. This topic can be viewed as an extension of spectral graph theory and the diffusion geometry framework to functional analysis and PDE-like evolutions. Some possible applications and numerical examples of the technique are provided, as is a general framework for approximating Hamilton-Jacobi equations on arbitrary grids in high dimensions, e.g., for control theory.
An article entitled “Non-local regularization of inverse problem,” by Peyre, Bougleux, and Cohenin (Lecture Notes in Computer Science, 2008, Volume 5304/2008, pp. 57-68), which is incorporated herein by reference, proposes a new framework to regularize linear inverse problems using the total variation on non-local graphs. A nonlocal graph allows adaptation of the penalization to the geometry of the underlying function to recover. A fast algorithm computes, iteratively, both the solution of the regularization process and the non-local graph adapted to this solution.
An article entitled “The split Bregman method for L1 regularized problems,” by Goldstein and Osher (SIAM Journal on Imaging Sciences, Volume 2, Issue 2, pp. 323-343), which is incorporated herein by reference, notes that the class of 11-regularized optimization problems has received much attention recently because of the introduction of “compressed sensing,” which allows images and signals to be reconstructed from small amounts of data. Despite this recent attention, many 11-regularized problems still remain difficult to solve, or require techniques that are very problem-specific. The authors show that Bregman iteration can be used to solve a wide variety of constrained optimization problems. Using this technique, the authors propose a “Split Bregman” method, which can solve a very broad class of 11-regularized problems.
In an article entitled “Bregmanized nonlocal regularization for reconvolution and sparse reconstruction,” by Zhang, Burgery, Bresson, and Osher (SIAM Journal on Imaging Sciences, Volume 3, Issue 3, July 2010), which is incorporated herein by reference, the authors propose two algorithms based on Bregman iteration and operator splitting technique for nonlocal TV regularization problems. The convergence of the algorithms is analyzed and applications to deconvolution and sparse reconstruction are presented.